Many games that use playing cards have been played for decades. Poker is a popular card game which has been played for many years throughout the world and has many variants (i.e.—texas hold'em poker, omaha poker, stud poker, draw poker, guts, razz, etc.). The term “poker” actually refers to a family of games that typically involve placing monetary bets.
Typically, poker games are played with a standard deck of 52 playing cards. The individual cards are ranked in the following order from highest to lowest: Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2. The suits are hearts (h), diamonds (d), clubs (c), and spades (s). The rank/suit combination of each of the 52 playing cards in the deck is unique, i.e., there is exactly one Ace of Clubs, there is exactly one Eight of Hearts, there is exactly one Jack of Spades, etc.
The objective of poker is generally to win the pot of money by obtaining the highest rank poker hand or by being the last player remaining (other players fold). The standard strength of 5-card poker hands rank in the following order from highest to lowest:    (1) Five of a Kind (five cards of the same rank, only possible when there are wild card);    (2) Straight Flush (five cards of the same suit in sequence);    (3) Four of a Kind (four cards of the same rank);    (4) Full House (three cards of one rank and two cards of another rank);    (5) Flush (five cards of the same suit);    (6) Straight (five cards in two or more suits, ranking consecutively);    (7) Three of a Kind (three cards of the same rank);    (8) Two Pair (two cards of one rank and two cards of another rank);    (9) One Pair (two cards of the same rank).    (10) High Card (highest rank card)
Most poker game variants follow the same basic pattern of play. For each hand dealt, one or more players are often required to post antes or make forced bets to create an initial stake for which the players will compete. The dealer shuffles the cards and the appropriate number of cards is dealt to each player one at a time. Cards may be dealt either face-up (common cards) or face-down (down or hole cards), depending on the variant of poker being played. After the initial deal, the first of what may be several rounds of wagering/betting begins. Between rounds, the players' hands develop in some way, often by being dealt additional cards or replacing cards previously dealt. At the end of each round of betting, all bets are gathered into the central pot (which may be comprised of main and side pots that are tracked separately). During a betting round, if a player makes a bet, opponents are required to fold, call, or raise. If one player bets and no opponents choose to match the bet, the hand ends immediately, the bettor is awarded the pot, no cards are required to be shown, and the next hand begins. At the end of the last betting round, if more than one player remains, there is a showdown in which the remaining players reveal their previously hidden cards to determine which player has the highest rank poker hand by combining the common cards (if any) with their down cards. Traditionally, the player with the highest rank poker hand (i.e., the high hand) for a given main or side pot is awarded that pot.
Poker has significantly grown in popularity to a multi-billion dollar industry. Modern poker tournament play became popular in casinos world-wide after the World Series of Poker© began in 1970. Poker's popularity experienced an unprecedented spike in the first years of the 21st century, largely because of the introduction of online poker and the invention of the hole-card camera, which turned the game into a spectator sport on television. Broadcasts of poker tournaments, such as the World Series of Poker© and the World Poker Tour© now bring in huge audiences for television networks. Due to poker's exciting stakes, simple rules, multiple game variants, social camaraderie, media coverage, and enjoyable competitive aspects, countless people are taking up the game of poker each year. At any given time many thousands of people are playing poker world-wide through local social gatherings or via commercial venues such as poker rooms, casinos, personal electronic games, and online poker websites utilizing computer networks and software.
Mathematical probability plays a central role in poker, especially in poker variants with multiple rounds of betting (e.g., Texas Hold'em or Omaha). Most skilled poker players estimate the mathematical probability of winning before acting during game play. Players able to consistently bet with a higher win probability than their opponents and fold with a lower win probability than their opponents, should win in the long run. The relevance and popularity of utilizing win probability in poker can be seen when watching win probabilities displayed to viewers during televised poker tournaments. Similarly, there are some online poker rooms that display win probability to players in all-in situations.
The win probability of a player if they do not fold can be directly calculated. In some cases the calculation is fairly complex, but generally the probability of a player winning at a certain point in the hand can be determined by dividing the number of outcomes that satisfy the condition being evaluated by the total number of possible outcomes. Therefore, to calculate a player's win probability in poker, one must determine the number of cards remaining that will give the player the highest rank poker hand at the showdown and divide that number by the total number of remaining cards that could be dealt.
To illustrate, we can analyze the following situation in Texas Hold'em: The flop has come 6(h) 4(c) 8(h) and the 2(s) was dealt on the turn; Player 1 has gone all-in holding A(d) A(s) and Player 2 has called holding K(h) Q(h). In Texas Hold'em one more common card will be dealt. The win probability of each player can now be calculated. In this situation hitting a flush via a heart on the river is the only way Player 2 can win, making exactly nine cards (outs) needed to achieve the high hand. Those nine outs are listed as follows: {2(h), 3(h) 4(h), 5(h), 7(h), 9(h), 10(h), J(h), A(h)}. Considering that Texas Hold'em is traditionally played using a standard 52 card deck, we can also determine that there are 44 possible outcomes for the final card at this point, determined by subtracting from 52 cards the 4 common cards already exposed and the 4 down cards of these two players that have now been exposed. (52−4−4=44). Therefore, Player 2's win probability is 9 divided by 44=20.45%, making Player 1's win probability 79.55% in this situation (subtract 20.45% from 100%).
Skilled and experienced poker players are able to approximate and sometimes exactly calculated their odds of winning before they make a wager. However, in many situations calculating the exact win probability without a computer is impossible. For example, in situations before the flop in Texas Holdem, the mathematics for computing all of the possible outcomes can be quite complex. Fortunately, a computer program can perform a brute force evaluation of the 1,712,304 possible boards for any given pair of starting hands in seconds. Thus, a computer program, such as any poker odds calculator commonly downloaded from the internet, is often needed to calculate and display the exact win probability of players.
A problem with poker games of multiple betting rounds is the occurrence of bad beats. A bad beat in poker generally refers to a player losing a hand that he was clearly favored to win. Receiving a bad beat is a great frustration to poker players because it often means that despite skillful play, an unlucky and often unfair outcome resulted. Many poker players would agree that there is nothing more frustrating in poker than wagering all of your money or chips you have in play (i.e., an all-in bet) as a significant mathematical favorite to win, only to get unlucky and lose the pot from being outdrawn. The higher a player's probability of winning the hand at the time of the all-in wager yet still losing at the showdown, the more frustrating the game can be for that player. Consequently, there is a need for an alternative method of conducting poker games which helps contend with bad beats in high win probability, all-in scenarios.
There is much debate as to what exactly constitutes a bad beat in poker. Historically, the occurrences of “bad beats” have been fairly subjective as players might disagree on a case by case basis as to whether or not a bad beat occurred. It is perhaps because of this subjectivity that few solutions have been developed that attempt to contend with bad beats. Thus, there is a need to officially identify bad beats in poker, in a manner that can't be contested by players. Once a bad beat can be officially and incontestably identified, it can be contended with or eliminated more easily.
An increasingly popular means used by card-rooms and casinos (online and off-line) to increase excitement and occasionally ease bad beat frustration for poker players is the use of Bad Beat jackpots. A Bad Beat jackpot is a prize that is paid to all players involved when a sufficiently strong hand is shown down and loses to an even stronger hand held by another player. Not all poker games offer Bad Beat jackpots, and those that do have specific requirements regarding how strong a losing hand must be to qualify for the jackpot, in addition to other requirements.
Though Bad Beat jackpots can be exciting marketing tools that can result in huge prizes for players lucky enough to satisfy the necessary conditions, they fail to mitigate the majority of bad beats. The criteria to satisfy a Bad Beat jackpot are rarely met (e.g., 4-of-a-kind must lose) and when conditions are met, payment to players does not come from the contested pot, but from a progressive prize pool that is usually funded from a rake on multiple tables over many hands of play. Thus, Bad Beat jackpots are generally not feasible to use in tournament play because there are no rakes. Most importantly, player win probability, which is essential in determining mathematically correct poker decisions, has nothing to do with the Bad Beat jackpot payout criteria. Therefore, a Bad Beat jackpot does not provide poker players with a sufficient, consistent solution to their bad beat frustrations.
In a similar manner, poker rooms occasionally offer smaller promotional bonuses when a strong hand loses. For example, some casinos pay out a bonus to any player who loses holding AA in Texas Holdem in a cash game. These bonuses are an attempt to mitigate frustration and make game play more exciting and enjoyable. However, similar to Bad Beat jackpots, an additional rake is necessary to fund these promotional bonuses, making them infeasible for tournament play. Also, these bonuses do not mitigate the majority of bad beats because player win probability is not considered in the payout criteria.
Consequently, there is a need for a method of conducting a poker game that considers player win probability to help alleviate bad beat frustration more consistently. Many poker players believe winning in poker should be a matter of skillful play and making great poker decisions based on win probability. Winning should be less reliant on the luck of the draw, especially in all-in situations. Unfortunately, in the short-term, it makes little difference how skillfully you play poker when bad beats are commonplace. In a time when the game of poker is considered a competitive sport world-wide, there is need for a method of conducting poker games to properly contend with bad beats.
Several variations, systems, and methods of conducting poker games that combine one or more of the features herein are described in U.S. Pat. Nos. 5,531,448; 6,042,118; 6,132,311; 6,651,983; 6,817,615; 6,938,900; 7,056,208; and US patent application number 2008/0012222. Most of these other games and methods modify the rules of game play in some manner when compared to conventional poker. However, many card room operators and players are not interested in a changing the rules of play for their favorite or most popular poker games.
In particular, U.S. Pat. No. 7,056,208 and US Patent App #20080012222 provide examples that attempt to contend with bad beats in poker. However, they both have flaws in addressing the bad beat problem. For example, U.S. Pat. No. 7,056,208 does not utilize win probability or statistics in any way to contend with bad beats; it only allows players the option to take a portion of their bet back at different points in the hand. Without utilizing win probability, bad beats are not properly and consistently identified and contended with. Furthermore, US Patent App document #20080012222 requires that players make a “declaration” of the best hand in order to achieve bad beat protection, but requiring a “declaration” changes the rules of play and adds unnecessary complexity to game play requirements. In addition, US Patent App #20080012222 does not contain any distinct bad beat cutoff percentage needed to properly and consistently identify Bad Beats. Thus, there remains a need for a system and method of conducting a poker game to contend with bad beats that does not change the rules of game play, but utilizes win probability and a distinct cutoff percentage to properly identify bad beats. The system and method should be applicable to any poker game variant utilizing common cards and multiple betting rounds.